A metal rod lies across frictionless parallel rails in a uniform magnetic field

Question

A metal rod lies across frictionless parallel rails in a uniform magnetic field that points normal to the plane of the rails. The rails are connected at one end, but not the other, so that a current can pass through the rod. The rod moves to the right at speed v, so that the area enclosed by the current loop is increasing. In order for the emf around the circuit to be zero, the magnitude of the magnetic field should
Choose one answer.
A. increase quadratically with time
B. not change
C. decrease quadratically with time
D. decrease linearly with time
E. increase linearly with time

Explanation / Answer

C decrease quadratically with time; the flux has to remain constant for there to be no emf; so B * area must be constant. If area doubles, B must be one half.

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